After the price shock I got this morning, I went on a more dedicated search for a less expensive, single-chip option for an ADC/DAC. I think I found one, with the NXP Semiconductor PCF8591T. It has four analog inputs, but it's not a problem to just tie the extra three to Ground; the $2-3 price tag also makes the board much, much less expensive, as well as much more open in terms of space.
I'm going to just hold on to this for a while before I send another quote request to PCBWay. Just from that one change, I do think I'll end up saving about $25 from that $138. I probably can also eliminate a few other components; I'll have to study the data sheets a bit more than I have. With any luck, I'll be able to bring the total with them to under $100 (meaning less than $20 per board).
Barring some calamity, I hopefully will have something truly presentable by the time a decision is made on the Take Flight With Feather contest (this is the version I'm now promoting for it -- unless, of course, it's too late to do something like that).